{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic HDDM Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following we will show an example session of using HDDM to analyze a real-world dataset. The main purpose is to provide an overview of some of the funcionality and interface. By no means, however, is it a complete overview of all the functionality in HDDM. For more information, including on how to use HDDM as a command-line utility, we refer to the online tutorial at http://ski.clps.brown.edu/hddm_docs/tutorial.html and the how-to at http://ski.clps.brown.edu/hddm_docs/howto.html. For a reference manual, see http://ski.clps.brown.edu/hddm_docs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we have to import the modules we are going to use so that they are available in our namespace. Pandas provides a table-oriented data-structure and matplotlib is a module for generating graphs and plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will import HDDM. At the time of this writing, this version was used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9.6\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import hddm\n",
    "\n",
    "print(hddm.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will load in a data set. The easiest way to get your data\n",
    "into HDDM is by storing it in a csv (comma-separated-value, see below) file. In this example we will be using data collected\n",
    "in a reward-based decision making experiment in our lab (Cavanagh et al 2011). In brief, subjects choose between two symbols that have different histories of reinforcement, which they first acquire through a learning phase: some symbols more often leads to wins  (W; 80%, 70% and 60% of trials in which they are selected), whereas others only lead to win on 40%, 30%, or 20% of the time and otherwise lead to losses (L). A test phase ensures in which subjects choose between all paired combination of symbols without feedback. These test trials can be devided into win-win (WW) trials, in which they select between two symbols that had led to wins before (but one more often than another); lose-lose trials (LL), and win-lose (WL) trials, which are the easiest because one symbol had been a winner most of the time. Thus WW and LL decisions together comprise high conflict (HC) test trials (although there are other differences between them, we don't focus on those here), whereas WL decisions are low conflict (LC).  The main hypothesis of the study was that high conflict trials induce an increase in the decision threshold, and that the mechanism for this threshold modulation depends on communication between mediofrontal cortex (which exhibits increased activity under conditions of choice uncertainty or conflict) and the subthalamic nucleus (STN) of the basal ganglia (which provides a temporary brake on response selection by increasing the decision threshold). The details of this mechanism are described in other modeling papers (e.g., Ratcliff & Frank 2012). Cavanagh et al 2011 tested this theory by measuring EEG activity over mid-frontal cortex, focusing on the theta band, given prior associations with conflict, and testing whether trial-to-trial variations in frontal theta were related to adjustments in decision threshold during high conflict trials. They tested the STN component of the theory by administering the same experiment to patients who had deep brain stimulation (dbs) of the STN, which interferes with normal processing.  \n",
    "\n",
    "The first ten lines of the data file look as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "subj_idx,stim,rt,response,theta,dbs,conf\n",
      "0,LL,1.21,1.0,0.65627512226100004,1,HC\n",
      "0,WL,1.6299999999999999,1.0,-0.32788867166199998,1,LC\n",
      "0,WW,1.03,1.0,-0.480284512399,1,HC\n",
      "0,WL,2.77,1.0,1.9274273452399999,1,LC\n",
      "0,WW,1.1399999999999999,0.0,-0.21323572605999999,1,HC\n",
      "0,WL,1.1499999999999999,1.0,-0.43620365940099998,1,LC\n",
      "0,LL,2.0,1.0,-0.27447891439400002,1,HC\n",
      "0,WL,1.04,0.0,0.66695707371400004,1,LC\n",
      "0,WW,0.85699999999999998,1.0,0.11861689909799999,1,HC\n"
     ]
    }
   ],
   "source": [
    "!head cavanagh_theta_nn.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the ``hddm.load_csv()`` function to load this file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = hddm.load_csv(\"./cavanagh_theta_nn.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subj_idx</th>\n",
       "      <th>stim</th>\n",
       "      <th>rt</th>\n",
       "      <th>response</th>\n",
       "      <th>theta</th>\n",
       "      <th>dbs</th>\n",
       "      <th>conf</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>LL</td>\n",
       "      <td>1.210</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.656275</td>\n",
       "      <td>1</td>\n",
       "      <td>HC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>WL</td>\n",
       "      <td>1.630</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.327889</td>\n",
       "      <td>1</td>\n",
       "      <td>LC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>WW</td>\n",
       "      <td>1.030</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.480285</td>\n",
       "      <td>1</td>\n",
       "      <td>HC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>WL</td>\n",
       "      <td>2.770</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.927427</td>\n",
       "      <td>1</td>\n",
       "      <td>LC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>WW</td>\n",
       "      <td>1.140</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.213236</td>\n",
       "      <td>1</td>\n",
       "      <td>HC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>WL</td>\n",
       "      <td>1.150</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.436204</td>\n",
       "      <td>1</td>\n",
       "      <td>LC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>LL</td>\n",
       "      <td>2.000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.274479</td>\n",
       "      <td>1</td>\n",
       "      <td>HC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>WL</td>\n",
       "      <td>1.040</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.666957</td>\n",
       "      <td>1</td>\n",
       "      <td>LC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>WW</td>\n",
       "      <td>0.857</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.118617</td>\n",
       "      <td>1</td>\n",
       "      <td>HC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>WL</td>\n",
       "      <td>1.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.823626</td>\n",
       "      <td>1</td>\n",
       "      <td>LC</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   subj_idx stim     rt  response     theta  dbs conf\n",
       "0         0   LL  1.210       1.0  0.656275    1   HC\n",
       "1         0   WL  1.630       1.0 -0.327889    1   LC\n",
       "2         0   WW  1.030       1.0 -0.480285    1   HC\n",
       "3         0   WL  2.770       1.0  1.927427    1   LC\n",
       "4         0   WW  1.140       0.0 -0.213236    1   HC\n",
       "5         0   WL  1.150       1.0 -0.436204    1   LC\n",
       "6         0   LL  2.000       1.0 -0.274479    1   HC\n",
       "7         0   WL  1.040       0.0  0.666957    1   LC\n",
       "8         0   WW  0.857       1.0  0.118617    1   HC\n",
       "9         0   WL  1.500       0.0  0.823626    1   LC"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the RT distributions of each individual subject using pandas' `groupby()` functionality. Because there are two possible responses (here we are using accuracy coding where 1 means the more rewarding symbol was chosen,  and 0 the less rewarding) we flip error RTs to be negative. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = hddm.utils.flip_errors(data)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, xlabel=\"RT\", ylabel=\"count\", title=\"RT distributions\")\n",
    "for i, subj_data in data.groupby(\"subj_idx\"):\n",
    "    subj_data.rt.hist(bins=20, histtype=\"step\", ax=ax)\n",
    "\n",
    "plt.savefig(\"hddm_demo_fig_00.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a hierarchical model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets fit a hierarchical DDM to this data set, starting off first with the simplest model that does not allow parameters to vary by condition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/afengler/opt/miniconda3/envs/hddmnn_tutorial/lib/python3.7/site-packages/scipy/optimize/optimize.py:2215: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  tmp2 = (x - v) * (fx - fw)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2000 of 2000 complete in 328.2 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14b8a1550>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Instantiate model object passing it our data (no need to call flip_errors() before passing it).\n",
    "\n",
    "# This will tailor an individual hierarchical DDM around your dataset.\n",
    "m = hddm.HDDM(data)\n",
    "# find a good starting point which helps with the convergence.\n",
    "m.find_starting_values()\n",
    "# start drawing 2000 samples and discarding 20 as burn-in (usually you want to have a longer burn-in period)\n",
    "m.sample(2000, burn=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now want to analyze our estimated model. `m.print_stats()` will print a table of summary statistics for each parameters' posterior. Because that is quite long we only print a subset of the parameters using pandas selection functionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>2.5q</th>\n",
       "      <th>25q</th>\n",
       "      <th>50q</th>\n",
       "      <th>75q</th>\n",
       "      <th>97.5q</th>\n",
       "      <th>mc err</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>1.97542</td>\n",
       "      <td>0.0940424</td>\n",
       "      <td>1.79218</td>\n",
       "      <td>1.91573</td>\n",
       "      <td>1.97419</td>\n",
       "      <td>2.03497</td>\n",
       "      <td>2.17103</td>\n",
       "      <td>0.00219092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a_std</th>\n",
       "      <td>0.33827</td>\n",
       "      <td>0.0770823</td>\n",
       "      <td>0.220386</td>\n",
       "      <td>0.285276</td>\n",
       "      <td>0.326261</td>\n",
       "      <td>0.380676</td>\n",
       "      <td>0.527831</td>\n",
       "      <td>0.00257471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a_subj.0</th>\n",
       "      <td>2.20059</td>\n",
       "      <td>0.0648662</td>\n",
       "      <td>2.07624</td>\n",
       "      <td>2.15591</td>\n",
       "      <td>2.20029</td>\n",
       "      <td>2.24381</td>\n",
       "      <td>2.33027</td>\n",
       "      <td>0.00200121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a_subj.1</th>\n",
       "      <td>2.11078</td>\n",
       "      <td>0.0644109</td>\n",
       "      <td>1.9864</td>\n",
       "      <td>2.06509</td>\n",
       "      <td>2.11072</td>\n",
       "      <td>2.15448</td>\n",
       "      <td>2.2363</td>\n",
       "      <td>0.00192041</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean        std      2.5q       25q       50q       75q  \\\n",
       "a         1.97542  0.0940424   1.79218   1.91573   1.97419   2.03497   \n",
       "a_std     0.33827  0.0770823  0.220386  0.285276  0.326261  0.380676   \n",
       "a_subj.0  2.20059  0.0648662   2.07624   2.15591   2.20029   2.24381   \n",
       "a_subj.1  2.11078  0.0644109    1.9864   2.06509   2.11072   2.15448   \n",
       "\n",
       "             97.5q      mc err  \n",
       "a          2.17103  0.00219092  \n",
       "a_std     0.527831  0.00257471  \n",
       "a_subj.0   2.33027  0.00200121  \n",
       "a_subj.1    2.2363  0.00192041  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats = m.gen_stats()\n",
    "stats[stats.index.isin([\"a\", \"a_std\", \"a_subj.0\", \"a_subj.1\"])]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the model estimated the group mean parameter for threshold `a`, group variability `a_std` and individual subject parameters `a_subj.0`. Other parameters are not shown here.\n",
    "\n",
    "The inference algorithm, MCMC, requires the chains of the model to have properly converged. While there is no way to guarantee convergence for a finite set of samples in MCMC,  there are many heuristics that allow you identify problems of convergence. One main analysis to look at is the trace, the autocorrelation, and the marginal posterior. You can plot these using the `plot_posteriors()` function. For the sake of brevity we only plot three here. In practice, however, you will always want to examine all of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting a\n",
      "Plotting a_std\n",
      "Plotting v\n",
      "Plotting t\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot_posteriors([\"a\", \"t\", \"v\", \"a_std\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, there are no drifts or large jumps in the trace. The autocorrelation is also very low."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gelman-Rubin statistic provides a more formal test for convergence that compares the intra-chain variance to the intra-chain variance of different runs of the same model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/afengler/opt/miniconda3/envs/hddmnn_tutorial/lib/python3.7/site-packages/scipy/optimize/optimize.py:2215: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  tmp2 = (x - v) * (fx - fw)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2000 of 2000 complete in 284.7 secNo model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n",
      " [-----------------100%-----------------] 2000 of 2000 complete in 314.5 secNo model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n",
      " [-----------------100%-----------------] 2000 of 2000 complete in 315.9 secNo model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n",
      " [-----------------100%-----------------] 2001 of 2000 complete in 224.1 secNo model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n",
      " [-----------------100%-----------------] 2001 of 2000 complete in 219.4 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'a': 0.9998303182212243,\n",
       " 'a_std': 1.000302900736453,\n",
       " 'a_subj.0': 0.9997302281455774,\n",
       " 'a_subj.1': 1.000210960096837,\n",
       " 'a_subj.2': 1.0000893900199943,\n",
       " 'a_subj.3': 1.0000376067768229,\n",
       " 'a_subj.4': 1.001288709935588,\n",
       " 'a_subj.5': 1.0000714056352387,\n",
       " 'a_subj.6': 1.0007846805440694,\n",
       " 'a_subj.7': 1.0004646343952772,\n",
       " 'a_subj.8': 1.0023483983425399,\n",
       " 'a_subj.9': 0.9997680215565935,\n",
       " 'a_subj.10': 0.9999889337044247,\n",
       " 'a_subj.11': 0.9999177658948148,\n",
       " 'a_subj.12': 1.000161133243421,\n",
       " 'a_subj.13': 1.0006337627947017,\n",
       " 'v': 0.9999569890550272,\n",
       " 'v_std': 0.9998101298324256,\n",
       " 'v_subj.0': 1.000091518454496,\n",
       " 'v_subj.1': 1.000439110921408,\n",
       " 'v_subj.2': 0.9998690492069756,\n",
       " 'v_subj.3': 0.9997795055437586,\n",
       " 'v_subj.4': 1.0005037511250383,\n",
       " 'v_subj.5': 1.0000666885634026,\n",
       " 'v_subj.6': 1.00088768074011,\n",
       " 'v_subj.7': 1.0001014006051618,\n",
       " 'v_subj.8': 0.9997181792217363,\n",
       " 'v_subj.9': 0.9998569851609095,\n",
       " 'v_subj.10': 1.0004447099624747,\n",
       " 'v_subj.11': 1.0003295986709129,\n",
       " 'v_subj.12': 0.9998716245752058,\n",
       " 'v_subj.13': 0.9999425880703108,\n",
       " 't': 1.0000918042254738,\n",
       " 't_std': 1.0003933181582687,\n",
       " 't_subj.0': 1.0000983747366763,\n",
       " 't_subj.1': 1.0002344516248227,\n",
       " 't_subj.2': 0.9999720509944335,\n",
       " 't_subj.3': 0.9997025634163307,\n",
       " 't_subj.4': 1.0014131825211063,\n",
       " 't_subj.5': 1.0002791965406719,\n",
       " 't_subj.6': 0.9999894930193757,\n",
       " 't_subj.7': 1.0002053674198979,\n",
       " 't_subj.8': 1.0019879801247795,\n",
       " 't_subj.9': 0.9999292140174104,\n",
       " 't_subj.10': 1.0002688771872774,\n",
       " 't_subj.11': 0.9998993705355971,\n",
       " 't_subj.12': 1.0007298255727528,\n",
       " 't_subj.13': 1.0006428388917614}"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models = []\n",
    "for i in range(5):\n",
    "    m = hddm.HDDM(data)\n",
    "    m.find_starting_values()\n",
    "    m.sample(2000, burn=500)\n",
    "    models.append(m)\n",
    "\n",
    "hddm.analyze.gelman_rubin(models)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might also be interested in how well the model fits the data. To inspect this visually you can call `plot_posterior_predictive()` to plot individual subject RT distributions in red on top of the predictive likelihood in blue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1008x720 with 14 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot_posterior_predictive(figsize=(14, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While visually the fit looks decent, we also have prior knowledge about our experiment which could be leveraged to improve the model. For example, we would expect that because LL and WW trials are harder than WL trials, drift rate would be higher in WL, which has lower uncertainty about the correct choice. (One could also develop a posterior predictive check statistic that would evaluate whether accuracy and mean RT are different in the different conditions. Since the parameters of the model were estimated to be the same across conditions, the posterior predictive distributions for these conditions would not look different from each other, whereas those in the data do. A formal posterior predictive check would thus show that the data violates the simple assumptions of the model. This is not evident above because we simply plotted the distributions collapsed across conditions). \n",
    "\n",
    "In any case, we can create a new model quite easily which estimates separate drift-rate `v` for those different conditions by using the `depends_on` keyword argument. This argument expects a Python `dict` which maps the parameter to be split to the column name containing the conditions we want to split by."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/afengler/opt/miniconda3/envs/hddmnn_tutorial/lib/python3.7/site-packages/scipy/optimize/optimize.py:2215: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  tmp2 = (x - v) * (fx - fw)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2000 of 2000 complete in 793.3 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14bbcc490>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_stim = hddm.HDDM(data, depends_on={\"v\": \"stim\"})\n",
    "m_stim.find_starting_values()\n",
    "m_stim.sample(2000, burn=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will skip examining the traces for this model and instead look at the posteriors of `v` for the different conditions. Below you can see that the drift rate for the low conflict WL condition is substantially greater than that for the other two conditions, which are fairly similar to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_WW, v_LL, v_WL = m_stim.nodes_db.node[[\"v(WW)\", \"v(LL)\", \"v(WL)\"]]\n",
    "hddm.analyze.plot_posterior_nodes([v_WW, v_LL, v_WL])\n",
    "plt.xlabel(\"drift-rate\")\n",
    "plt.ylabel(\"Posterior probability\")\n",
    "plt.title(\"Posterior of drift-rate group means\")\n",
    "plt.savefig(\"hddm_demo_fig_06.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While it would be easy to provide syntacic sugar for the above expression there are many cases where you want access to the underlying distributions. These are stored inside of `nodes_db` which is a pandas `DataFrame` containing information about each distribution. Here we retrieve the actual node objects containing the trace from the `node` colum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One benefit of estimating the model in a Bayesian framework is that we can do significance testing directly on the posterior rather than relying on frequentist statistics (See Kruschke's book for many examples of the advantages of this approach). For example, we might be interested in whether the drift-rate for WW is larger than that for LL, or whether drift-rate for LL is larger than WL. The below code allows us to examine the proportion of the posteriors in which the drift rate for one condition is greater than the other. It can be seen that the posteriors for LL do not overlap at all for WL, and thus the probability that LL is greater than WL should be near zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(WW > LL) =  0.36473684210526314\n",
      "P(LL > WL) =  0.0\n"
     ]
    }
   ],
   "source": [
    "print(\"P(WW > LL) = \", (v_WW.trace() > v_LL.trace()).mean())\n",
    "print(\"P(LL > WL) = \", (v_LL.trace() > v_WL.trace()).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets compare the two models using the deviance information criterion (DIC; lower is better). Note that the DIC measures the fit of the model to the data, penalizing for complexity in the addition of degrees of freedom (the model with three drift rates has more dF than the model with one). The DIC is known to be somewhat biased in selecting the model with greater complexity, although alternative forms exist (see Plummer 2008). One should use the DIC with caution, although other forms of model comparison such as the Bayes Factor (BF) have other problems, such as being overly sensitive to the prior parameter distributions of the models. Future versions of HDDM will include the partial Bayes Factor, which allows the BF to be computed based on informative priors taken from a subset of the data, and which we generally believe to provide a better measure of model fit. Nevertheless, DIC can be a useful metric with these caveats in mind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lumped model DIC: 10974.090050\n",
      "Stimulus model DIC: 10786.243737\n"
     ]
    }
   ],
   "source": [
    "print(\"Lumped model DIC: %f\" % m.dic)\n",
    "print(\"Stimulus model DIC: %f\" % m_stim.dic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Within-subject effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that while the `m_stim` model we created above estimates different drift-rates `v` for each subject, it implicitly assumes that the different conditions are completely independent of each other, because each drift rate was sampled from a separate group prior. However, there may be individual differences in overall performance, and if so it is reasonable to assume that someone who would be better at `WL` would also be better at `LL`. To model this intuition we can use a within-subject model where an intercept is used to capture overall performance in the 'WL' condition as a baseline, and then the other `LL` and `WW` conditions are expressed relative to `WL`. (Perhaps every subject has a higher drift in WL than LL but there is huge variance in their overall drift rates. In this scenario, the earlier model would not have the power to detect the effect of condition on this within subject effect, because there would be large posterior variance in all of the drift rates, which would then overlap with each other. In contrast, the within-subject model would estimate large variance in the intercept but still allow the model to infer a non-zero effect of condition with high precision).\n",
    "\n",
    "`HDDM` supports this via the `patsy` module which transforms model strings to design matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DesignMatrix with shape (10, 3)\n",
       "  Intercept  C(stim, Treatment('WL'))[T.LL]  C(stim, Treatment('WL'))[T.WW]\n",
       "          1                               1                               0\n",
       "          1                               0                               0\n",
       "          1                               0                               1\n",
       "          1                               0                               0\n",
       "          1                               0                               1\n",
       "          1                               0                               0\n",
       "          1                               1                               0\n",
       "          1                               0                               0\n",
       "          1                               0                               1\n",
       "          1                               0                               0\n",
       "  Terms:\n",
       "    'Intercept' (column 0)\n",
       "    \"C(stim, Treatment('WL'))\" (columns 1:3)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from patsy import dmatrix\n",
    "\n",
    "dmatrix(\"C(stim, Treatment('WL'))\", data.head(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Patsy` model specifications can be passed to the `HDDMRegressor` class as part of a descriptor that contains the string describing the linear model and the `outcome` variable that should be replaced with the output of the linear model -- in this case `v`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n"
     ]
    }
   ],
   "source": [
    "m_within_subj = hddm.HDDMRegressor(data, \"v ~ C(stim, Treatment('WL'))\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2001 of 2000 complete in 1423.8 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14bb55350>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_within_subj.sample(2000, burn=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_WL, v_LL, v_WW = m_within_subj.nodes_db.loc[\n",
    "    [\n",
    "        \"v_Intercept\",\n",
    "        \"v_C(stim, Treatment('WL'))[T.LL]\",\n",
    "        \"v_C(stim, Treatment('WL'))[T.WW]\",\n",
    "    ],\n",
    "    \"node\",\n",
    "]\n",
    "hddm.analyze.plot_posterior_nodes([v_WL, v_LL, v_WW])\n",
    "plt.xlabel(\"drift-rate\")\n",
    "plt.ylabel(\"Posterior probability\")\n",
    "plt.title(\"Group mean posteriors of within-subject drift-rate effects.\")\n",
    "plt.savefig(\"hddm_demo_fig_07.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in the above plot `LL` and `WW` are expressed relative to the `WL` condition (i.e. `v_Intercept`). You can see that the overall drift rate intercept, here applying to WL condition, is positive (mode value roughly 0.7), whereas the within subject effects of condition (WW and LL) are negative and do not overlap with zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting regression models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned above, cognitive neuroscience has embraced the DDM as it enables to link psychological processes to cognitive brain measures. The Cavanagh et al (2011) study is a great example of this. EEG recordings provided a trial-ty-trial measure of brain activity (frontal theta), and it was found that this activity correlated with increases in decision threshold in high conflict trials.  Note that the data set and results exhibit more features than we consider here for the time being (specifically the manipulation of deep brain stimulation), but for illustrative purposes, we replicate here that main theta-threshold relationship in a model restricted to participants without brain stimulation.  For more information, see http://ski.clps.brown.edu/papers/Cavanagh_DBSEEG.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n"
     ]
    }
   ],
   "source": [
    "m_reg = hddm.HDDMRegressor(\n",
    "    data[data.dbs == 0], \"a ~ theta:C(conf, Treatment('LC'))\", depends_on={\"v\": \"stim\"}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of estimating one static threshold per subject across trials, this model assumes the threshold to vary on each trial according to the linear model specified above (as a function of their measured theta activity). We also test whether this effect interacts with decision conflict. For the stimuli we use dummy treatment coding with the intercept being set on the WL condition. Internally, HDDM uses Patsy for the linear model specification, see the [Patsy documentation](https://patsy.readthedocs.org/en/latest/) for more details. The output notifies us about the different variables that being estimated as part of the linear model. The Cavanagh paper, and results shown later below, illustrate that this brain/behavior relationship differs as a function of whether patients are on or off STN deep brain stimulation, as hypothesized by the model that STN is responsible for increasing the decision threshold when cortical theta rises)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [--------------   38%                  ] 766 of 2000 complete in 854.2 secHalting at iteration  765  of  2000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14b3caf50>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_reg.sample(2000, burn=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(a_theta < 0) =  0.02375\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f35f1fd62b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = m_reg.nodes_db.node[\"a_theta:C(conf, Treatment('LC'))[HC]\"]\n",
    "hddm.analyze.plot_posterior_nodes([theta], bins=20)\n",
    "plt.xlabel(\"Theta coeffecient in \")\n",
    "print(\"P(a_theta < 0) = \", (theta.trace() < 0).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above posterior shows that the effect of trial to trial variations in frontal theta are to increase the estimated decision threshold: the regression coefficient is positive, and more than 96% of it is greater than zero. \n",
    "\n",
    "As noted above, this experiment also tested patients on deep brain stimulation (dbs). The full model in the paper thus allowed an additional factor to estimate how dbs interacts with theta-threshold relationship. Here we show for illustrative purposes that we can capture the same effect by simply fitting a separate model to data only including the case when dbs was turned on. You should see below that in this case, the influence of theta on threshold reverses. This exercise thus shows that HDDM can be used both to assess the influence of trial-by-trial brain measures on DDM parameters, but also how parameters vary when brain state is manipulated.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n"
     ]
    }
   ],
   "source": [
    "m_reg_off = hddm.HDDMRegressor(\n",
    "    data[data.dbs == 1], \"a ~ theta:C(conf, Treatment('LC'))\", depends_on={\"v\": \"stim\"}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2001 of 2000 complete in 1098.3 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14c398b10>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_reg_off.sample(2000, burn=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(a_theta > 0) =  0.05421052631578947\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = m_reg_off.nodes_db.node[\"a_theta:C(conf, Treatment('LC'))[HC]\"]\n",
    "hddm.analyze.plot_posterior_nodes([theta], bins=10)\n",
    "print(\"P(a_theta > 0) = \", (theta.trace() > 0).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dealing with outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is common to have outliers in any data set and RT data is no exception. Outliers present a serious challenge to likelihood-based approaches, as used in HDDM. Consider the possibility that 5% of trials are not generated by the DDM process, but by some other process (e.g. due to an attentional lapse). The observed data in those trials may be very unlikely given the best DDM parameters that fit 95% of the data. In the extreme case, the likelihood of a single trial may be zero (e.g. if subjects respond very quickly, faster than the non-decision time `t` parameter that would fit the rest of the data). Thus this single outlier would force the DDM parameters to adjust substantially.  To see the effect of this we will generate data with outliers, but fit a standard DDM model without taking outliers into account."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/afengler/opt/miniconda3/envs/hddmnn_tutorial/lib/python3.7/site-packages/pandas/core/indexing.py:671: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self._setitem_with_indexer(indexer, value)\n"
     ]
    }
   ],
   "source": [
    "outlier_data, params = hddm.generate.gen_rand_data(\n",
    "    params={\"a\": 2, \"t\": 0.4, \"v\": 0.5}, size=200, n_fast_outliers=10\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n",
      " [-----------------100%-----------------] 2000 of 2000 complete in 16.5 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14b9a9810>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_no_outlier = hddm.HDDM(outlier_data, p_outlier=0.0)\n",
    "m_no_outlier.sample(2000, burn=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/afengler/OneDrive/project_hddm_extension/kabuki/kabuki/analyze.py:589: UserWarning: Too many nodes. Consider increasing number of columns.\n",
      "  warnings.warn('Too many nodes. Consider increasing number of columns.')\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m_no_outlier.plot_posterior_predictive()\n",
    "plt.title(\"Posterior predictive\")\n",
    "plt.xlabel(\"RT\")\n",
    "plt.ylabel(\"Probability density\")\n",
    "plt.savefig(\"hddm_demo_fig_10.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the predictive likelihood does not fit the RT data very well. The model predicts far more RTs near the leading edge of the distribution than are actually observed. This is because non-decision time `t` is forced to be estimated small enough to account for a few fast RTs.  \n",
    "\n",
    "What we can do instead is fit a mixture model which assumes that outliers come from a uniform distribution. (Note, outliers do not have to be very fast or very slow, and the above example is just an obvious illustration. Some proportion of the trials can be assumed to simply come from a different process for which we make no assumptions about its generation, and hence use a uniform distribution. This allows the model to find the best DDM parameters that capture the majority of trials).   Here, we specify that we expect roughly 5% outliers in our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No model attribute --> setting up standard HDDM\n",
      "Set model to ddm\n",
      " [-----------------100%-----------------] 2000 of 2000 complete in 19.2 sec"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pymc.MCMC.MCMC at 0x14c33a690>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_outlier = hddm.HDDM(outlier_data, p_outlier=0.05)\n",
    "m_outlier.sample(2000, burn=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/afengler/OneDrive/project_hddm_extension/kabuki/kabuki/analyze.py:589: UserWarning: Too many nodes. Consider increasing number of columns.\n",
      "  warnings.warn('Too many nodes. Consider increasing number of columns.')\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m_outlier.plot_posterior_predictive()\n",
    "plt.title(\"Posterior predictive\")\n",
    "plt.xlabel(\"RT\")\n",
    "plt.ylabel(\"Probability density\")\n",
    "plt.savefig(\"hddm_demo_fig_11.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the model provides a much better fit. The outlier RTs are having less of an effect because they get assigned to the uniform outlier distribution. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
